Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting tr
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Specific criteria for BCS-type cuprate superconductivity and peculiar isotope effects on the critical superconducting transition temperature S DZHUMANOV1,∗ , B L OKSENGENDLER2 and SH S DJUMANOV1 1 Institute
of Nuclear Physics, Uzbek Academy of Sciences, 100214 Ulugbek, Tashkent, Uzbekistan of Ion-Plasma and Laser Technologies, Uzbek Academy of Sciences, 100125 Tashkent, Uzbekistan ∗ Corresponding author. E-mail: [email protected] 2 Institute
MS received 13 September 2018; accepted 9 October 2019 Abstract. So far, many researchers have been misled to believe that the Bardeen–Cooper–Schrieffer (BCS)-like (sor d-wave) pairing theory is adequate for explaining high-Tc superconductivity in doped cuprates from underdoped to overdoped regime. We show that the doped cuprates, depending on the Fermi energy (εF ) and the energy (εA ) of the effective attraction between pairing carriers, might be either unconventional (non-BCS-type) superconductors (at intermediate doping) or BCS-type superconductors (at higher doping). We argue that specific criteria for BCS-type superconductivity formulated in terms of two ratios εA /εF and /εF (where is the BCS-like gap) must be met in these systems. We demonstrate that these criteria are satisfied only in overdoped cuprates but not in underdoped and optimally doped cuprates, where the origin of high-Tc superconductivity is quite different from the BCS-type (s- or d-wave) superconductivity. The BCS-like pairing theory is then used to calculate the critical superconducting transition temperature (Tc ) and the peculiar oxygen and copper isotope effects on Tc in overdoped cuprates. Keywords. Cuprate superconductors; doping effects; specific criteria for BCS-type cuprate superconductivity; oxygen and copper isotope effects on Tc . PACS Nos 74.20.Fg; 74.62.Dh; 74.72.−h
1. Introduction The superconducivity in ordinary metals with large Fermi energies (εF > 1 eV) is now well described in terms of the Bardeen–Cooper–Schrieffer (BCS) condensation of Cooper pairs at the critical superconducting transition temperature (Tc ). In these weak-coupling superconductors, the formation of Cooper pairs and their BCS condensation into a superfluid Fermi liquid state occur simultaneously at Tc . The occurrence of such a BCS-type Fermi liquid superconductivity in other systems (which might be fermion superconductors [1]) is also of fundamental interest, especially in the physics of doped semiconductors [2] and doped Mott insulators [3–6] (e.g., the undoped copper oxides (cuprates) are typical Mott insulators). The situation, however, is different in doped cuprates in which the Fermi energy (εF ) is small and comparable with the energy h¯ ω0 of the high-frequency optical phonons. The undoped cuprates with charge-transfer gaps CT ∼ = 1.5–2.0 0123456789().: V,-vol
eV [3,5] are Mott insulators and the doped cuprates behave like doped semiconductors (e.g., Si and Ge) [7,8]. Hole doping of the cuprates produces free holes in the oxygen valence band and the large ionicity of these mat
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